Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(172\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53688 | −1.79385 | −0.896924 | − | 0.442185i | \(-0.854203\pi\) | ||||
−0.896924 | + | 0.442185i | \(0.854203\pi\) | |||||||
\(3\) | −2.79023 | −1.61094 | −0.805470 | − | 0.592637i | \(-0.798087\pi\) | ||||
−0.805470 | + | 0.592637i | \(0.798087\pi\) | |||||||
\(4\) | 4.43578 | 2.21789 | ||||||||
\(5\) | 3.33172 | 1.48999 | 0.744996 | − | 0.667069i | \(-0.232452\pi\) | ||||
0.744996 | + | 0.667069i | \(0.232452\pi\) | |||||||
\(6\) | 7.07848 | 2.88978 | ||||||||
\(7\) | −4.26650 | −1.61259 | −0.806293 | − | 0.591517i | \(-0.798529\pi\) | ||||
−0.806293 | + | 0.591517i | \(0.798529\pi\) | |||||||
\(8\) | −6.17928 | −2.18471 | ||||||||
\(9\) | 4.78538 | 1.59513 | ||||||||
\(10\) | −8.45219 | −2.67282 | ||||||||
\(11\) | −4.42179 | −1.33322 | −0.666610 | − | 0.745407i | \(-0.732255\pi\) | ||||
−0.666610 | + | 0.745407i | \(0.732255\pi\) | |||||||
\(12\) | −12.3768 | −3.57288 | ||||||||
\(13\) | 6.67188 | 1.85045 | 0.925223 | − | 0.379424i | \(-0.123878\pi\) | ||||
0.925223 | + | 0.379424i | \(0.123878\pi\) | |||||||
\(14\) | 10.8236 | 2.89273 | ||||||||
\(15\) | −9.29627 | −2.40029 | ||||||||
\(16\) | 6.80456 | 1.70114 | ||||||||
\(17\) | −2.89072 | −0.701102 | −0.350551 | − | 0.936544i | \(-0.614006\pi\) | ||||
−0.350551 | + | 0.936544i | \(0.614006\pi\) | |||||||
\(18\) | −12.1399 | −2.86141 | ||||||||
\(19\) | −7.22734 | −1.65807 | −0.829033 | − | 0.559200i | \(-0.811108\pi\) | ||||
−0.829033 | + | 0.559200i | \(0.811108\pi\) | |||||||
\(20\) | 14.7788 | 3.30463 | ||||||||
\(21\) | 11.9045 | 2.59778 | ||||||||
\(22\) | 11.2176 | 2.39159 | ||||||||
\(23\) | −3.14906 | −0.656625 | −0.328313 | − | 0.944569i | \(-0.606480\pi\) | ||||
−0.328313 | + | 0.944569i | \(0.606480\pi\) | |||||||
\(24\) | 17.2416 | 3.51943 | ||||||||
\(25\) | 6.10037 | 1.22007 | ||||||||
\(26\) | −16.9258 | −3.31942 | ||||||||
\(27\) | −4.98161 | −0.958711 | ||||||||
\(28\) | −18.9252 | −3.57653 | ||||||||
\(29\) | −9.62452 | −1.78723 | −0.893614 | − | 0.448837i | \(-0.851838\pi\) | ||||
−0.893614 | + | 0.448837i | \(0.851838\pi\) | |||||||
\(30\) | 23.5835 | 4.30575 | ||||||||
\(31\) | 8.77694 | 1.57639 | 0.788193 | − | 0.615428i | \(-0.211017\pi\) | ||||
0.788193 | + | 0.615428i | \(0.211017\pi\) | |||||||
\(32\) | −4.90381 | −0.866880 | ||||||||
\(33\) | 12.3378 | 2.14774 | ||||||||
\(34\) | 7.33341 | 1.25767 | ||||||||
\(35\) | −14.2148 | −2.40274 | ||||||||
\(36\) | 21.2269 | 3.53781 | ||||||||
\(37\) | −0.615614 | −0.101206 | −0.0506031 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506031 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(38\) | 18.3349 | 2.97432 | ||||||||
\(39\) | −18.6161 | −2.98096 | ||||||||
\(40\) | −20.5876 | −3.25519 | ||||||||
\(41\) | −5.40120 | −0.843526 | −0.421763 | − | 0.906706i | \(-0.638588\pi\) | ||||
−0.421763 | + | 0.906706i | \(0.638588\pi\) | |||||||
\(42\) | −30.2004 | −4.66002 | ||||||||
\(43\) | −5.31325 | −0.810263 | −0.405131 | − | 0.914258i | \(-0.632774\pi\) | ||||
−0.405131 | + | 0.914258i | \(0.632774\pi\) | |||||||
\(44\) | −19.6141 | −2.95693 | ||||||||
\(45\) | 15.9435 | 2.37672 | ||||||||
\(46\) | 7.98881 | 1.17789 | ||||||||
\(47\) | 5.48086 | 0.799465 | 0.399733 | − | 0.916632i | \(-0.369103\pi\) | ||||
0.399733 | + | 0.916632i | \(0.369103\pi\) | |||||||
\(48\) | −18.9863 | −2.74043 | ||||||||
\(49\) | 11.2030 | 1.60043 | ||||||||
\(50\) | −15.4759 | −2.18863 | ||||||||
\(51\) | 8.06576 | 1.12943 | ||||||||
\(52\) | 29.5949 | 4.10408 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 12.6378 | 1.71978 | ||||||||
\(55\) | −14.7322 | −1.98649 | ||||||||
\(56\) | 26.3639 | 3.52302 | ||||||||
\(57\) | 20.1659 | 2.67104 | ||||||||
\(58\) | 24.4163 | 3.20601 | ||||||||
\(59\) | −8.73398 | −1.13707 | −0.568533 | − | 0.822660i | \(-0.692489\pi\) | ||||
−0.568533 | + | 0.822660i | \(0.692489\pi\) | |||||||
\(60\) | −41.2362 | −5.32357 | ||||||||
\(61\) | −9.66490 | −1.23746 | −0.618732 | − | 0.785602i | \(-0.712353\pi\) | ||||
−0.618732 | + | 0.785602i | \(0.712353\pi\) | |||||||
\(62\) | −22.2661 | −2.82780 | ||||||||
\(63\) | −20.4168 | −2.57228 | ||||||||
\(64\) | −1.16872 | −0.146090 | ||||||||
\(65\) | 22.2288 | 2.75715 | ||||||||
\(66\) | −31.2996 | −3.85271 | ||||||||
\(67\) | −5.02390 | −0.613767 | −0.306883 | − | 0.951747i | \(-0.599286\pi\) | ||||
−0.306883 | + | 0.951747i | \(0.599286\pi\) | |||||||
\(68\) | −12.8226 | −1.55497 | ||||||||
\(69\) | 8.78661 | 1.05778 | ||||||||
\(70\) | 36.0613 | 4.31015 | ||||||||
\(71\) | −15.3294 | −1.81926 | −0.909630 | − | 0.415419i | \(-0.863635\pi\) | ||||
−0.909630 | + | 0.415419i | \(0.863635\pi\) | |||||||
\(72\) | −29.5702 | −3.48488 | ||||||||
\(73\) | −2.68984 | −0.314822 | −0.157411 | − | 0.987533i | \(-0.550315\pi\) | ||||
−0.157411 | + | 0.987533i | \(0.550315\pi\) | |||||||
\(74\) | 1.56174 | 0.181549 | ||||||||
\(75\) | −17.0214 | −1.96547 | ||||||||
\(76\) | −32.0589 | −3.67740 | ||||||||
\(77\) | 18.8656 | 2.14993 | ||||||||
\(78\) | 47.2268 | 5.34738 | ||||||||
\(79\) | −0.747072 | −0.0840521 | −0.0420261 | − | 0.999117i | \(-0.513381\pi\) | ||||
−0.0420261 | + | 0.999117i | \(0.513381\pi\) | |||||||
\(80\) | 22.6709 | 2.53468 | ||||||||
\(81\) | −0.456299 | −0.0506999 | ||||||||
\(82\) | 13.7022 | 1.51316 | ||||||||
\(83\) | 2.15515 | 0.236559 | 0.118279 | − | 0.992980i | \(-0.462262\pi\) | ||||
0.118279 | + | 0.992980i | \(0.462262\pi\) | |||||||
\(84\) | 52.8057 | 5.76158 | ||||||||
\(85\) | −9.63107 | −1.04464 | ||||||||
\(86\) | 13.4791 | 1.45349 | ||||||||
\(87\) | 26.8546 | 2.87912 | ||||||||
\(88\) | 27.3235 | 2.91269 | ||||||||
\(89\) | −12.3172 | −1.30562 | −0.652812 | − | 0.757520i | \(-0.726411\pi\) | ||||
−0.652812 | + | 0.757520i | \(0.726411\pi\) | |||||||
\(90\) | −40.4469 | −4.26348 | ||||||||
\(91\) | −28.4656 | −2.98400 | ||||||||
\(92\) | −13.9685 | −1.45632 | ||||||||
\(93\) | −24.4897 | −2.53946 | ||||||||
\(94\) | −13.9043 | −1.43412 | ||||||||
\(95\) | −24.0795 | −2.47050 | ||||||||
\(96\) | 13.6828 | 1.39649 | ||||||||
\(97\) | 12.0937 | 1.22793 | 0.613964 | − | 0.789334i | \(-0.289574\pi\) | ||||
0.613964 | + | 0.789334i | \(0.289574\pi\) | |||||||
\(98\) | −28.4208 | −2.87093 | ||||||||
\(99\) | −21.1599 | −2.12665 | ||||||||
\(100\) | 27.0599 | 2.70599 | ||||||||
\(101\) | 11.1599 | 1.11046 | 0.555228 | − | 0.831698i | \(-0.312631\pi\) | ||||
0.555228 | + | 0.831698i | \(0.312631\pi\) | |||||||
\(102\) | −20.4619 | −2.02603 | ||||||||
\(103\) | 4.73867 | 0.466915 | 0.233458 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233458 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(104\) | −41.2274 | −4.04268 | ||||||||
\(105\) | 39.6625 | 3.87067 | ||||||||
\(106\) | 2.53688 | 0.246404 | ||||||||
\(107\) | 17.3994 | 1.68206 | 0.841031 | − | 0.540987i | \(-0.181949\pi\) | ||||
0.841031 | + | 0.540987i | \(0.181949\pi\) | |||||||
\(108\) | −22.0973 | −2.12631 | ||||||||
\(109\) | −7.22806 | −0.692323 | −0.346161 | − | 0.938175i | \(-0.612515\pi\) | ||||
−0.346161 | + | 0.938175i | \(0.612515\pi\) | |||||||
\(110\) | 37.3738 | 3.56345 | ||||||||
\(111\) | 1.71770 | 0.163037 | ||||||||
\(112\) | −29.0317 | −2.74323 | ||||||||
\(113\) | −16.3070 | −1.53403 | −0.767017 | − | 0.641627i | \(-0.778260\pi\) | ||||
−0.767017 | + | 0.641627i | \(0.778260\pi\) | |||||||
\(114\) | −51.1586 | −4.79144 | ||||||||
\(115\) | −10.4918 | −0.978366 | ||||||||
\(116\) | −42.6922 | −3.96387 | ||||||||
\(117\) | 31.9274 | 2.95169 | ||||||||
\(118\) | 22.1571 | 2.03972 | ||||||||
\(119\) | 12.3332 | 1.13059 | ||||||||
\(120\) | 57.4442 | 5.24392 | ||||||||
\(121\) | 8.55224 | 0.777476 | ||||||||
\(122\) | 24.5187 | 2.21982 | ||||||||
\(123\) | 15.0706 | 1.35887 | ||||||||
\(124\) | 38.9326 | 3.49625 | ||||||||
\(125\) | 3.66613 | 0.327909 | ||||||||
\(126\) | 51.7951 | 4.61427 | ||||||||
\(127\) | −7.93101 | −0.703763 | −0.351881 | − | 0.936045i | \(-0.614458\pi\) | ||||
−0.351881 | + | 0.936045i | \(0.614458\pi\) | |||||||
\(128\) | 12.7725 | 1.12894 | ||||||||
\(129\) | 14.8252 | 1.30528 | ||||||||
\(130\) | −56.3920 | −4.94590 | ||||||||
\(131\) | −1.73019 | −0.151168 | −0.0755838 | − | 0.997139i | \(-0.524082\pi\) | ||||
−0.0755838 | + | 0.997139i | \(0.524082\pi\) | |||||||
\(132\) | 54.7278 | 4.76344 | ||||||||
\(133\) | 30.8355 | 2.67377 | ||||||||
\(134\) | 12.7450 | 1.10100 | ||||||||
\(135\) | −16.5973 | −1.42847 | ||||||||
\(136\) | 17.8626 | 1.53170 | ||||||||
\(137\) | 1.56124 | 0.133386 | 0.0666928 | − | 0.997774i | \(-0.478755\pi\) | ||||
0.0666928 | + | 0.997774i | \(0.478755\pi\) | |||||||
\(138\) | −22.2906 | −1.89750 | ||||||||
\(139\) | −0.245290 | −0.0208053 | −0.0104026 | − | 0.999946i | \(-0.503311\pi\) | ||||
−0.0104026 | + | 0.999946i | \(0.503311\pi\) | |||||||
\(140\) | −63.0536 | −5.32900 | ||||||||
\(141\) | −15.2929 | −1.28789 | ||||||||
\(142\) | 38.8888 | 3.26348 | ||||||||
\(143\) | −29.5016 | −2.46705 | ||||||||
\(144\) | 32.5624 | 2.71353 | ||||||||
\(145\) | −32.0662 | −2.66295 | ||||||||
\(146\) | 6.82381 | 0.564743 | ||||||||
\(147\) | −31.2590 | −2.57820 | ||||||||
\(148\) | −2.73073 | −0.224464 | ||||||||
\(149\) | 14.9407 | 1.22399 | 0.611995 | − | 0.790862i | \(-0.290367\pi\) | ||||
0.611995 | + | 0.790862i | \(0.290367\pi\) | |||||||
\(150\) | 43.1814 | 3.52575 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 44.6598 | 3.62239 | ||||||||
\(153\) | −13.8332 | −1.11835 | ||||||||
\(154\) | −47.8597 | −3.85665 | ||||||||
\(155\) | 29.2423 | 2.34880 | ||||||||
\(156\) | −82.5767 | −6.61143 | ||||||||
\(157\) | 1.42369 | 0.113623 | 0.0568115 | − | 0.998385i | \(-0.481907\pi\) | ||||
0.0568115 | + | 0.998385i | \(0.481907\pi\) | |||||||
\(158\) | 1.89523 | 0.150777 | ||||||||
\(159\) | 2.79023 | 0.221280 | ||||||||
\(160\) | −16.3381 | −1.29164 | ||||||||
\(161\) | 13.4355 | 1.05886 | ||||||||
\(162\) | 1.15758 | 0.0909479 | ||||||||
\(163\) | 16.7984 | 1.31575 | 0.657876 | − | 0.753126i | \(-0.271455\pi\) | ||||
0.657876 | + | 0.753126i | \(0.271455\pi\) | |||||||
\(164\) | −23.9585 | −1.87085 | ||||||||
\(165\) | 41.1061 | 3.20011 | ||||||||
\(166\) | −5.46737 | −0.424350 | ||||||||
\(167\) | 2.09222 | 0.161901 | 0.0809503 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809503 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(168\) | −73.5613 | −5.67538 | ||||||||
\(169\) | 31.5139 | 2.42415 | ||||||||
\(170\) | 24.4329 | 1.87392 | ||||||||
\(171\) | −34.5856 | −2.64482 | ||||||||
\(172\) | −23.5684 | −1.79707 | ||||||||
\(173\) | −8.43659 | −0.641422 | −0.320711 | − | 0.947177i | \(-0.603922\pi\) | ||||
−0.320711 | + | 0.947177i | \(0.603922\pi\) | |||||||
\(174\) | −68.1270 | −5.16469 | ||||||||
\(175\) | −26.0272 | −1.96747 | ||||||||
\(176\) | −30.0883 | −2.26799 | ||||||||
\(177\) | 24.3698 | 1.83175 | ||||||||
\(178\) | 31.2474 | 2.34209 | ||||||||
\(179\) | −1.23546 | −0.0923423 | −0.0461711 | − | 0.998934i | \(-0.514702\pi\) | ||||
−0.0461711 | + | 0.998934i | \(0.514702\pi\) | |||||||
\(180\) | 70.7220 | 5.27131 | ||||||||
\(181\) | 11.5450 | 0.858132 | 0.429066 | − | 0.903273i | \(-0.358843\pi\) | ||||
0.429066 | + | 0.903273i | \(0.358843\pi\) | |||||||
\(182\) | 72.2138 | 5.35284 | ||||||||
\(183\) | 26.9673 | 1.99348 | ||||||||
\(184\) | 19.4589 | 1.43453 | ||||||||
\(185\) | −2.05105 | −0.150797 | ||||||||
\(186\) | 62.1275 | 4.55541 | ||||||||
\(187\) | 12.7822 | 0.934723 | ||||||||
\(188\) | 24.3119 | 1.77313 | ||||||||
\(189\) | 21.2540 | 1.54600 | ||||||||
\(190\) | 61.0869 | 4.43171 | ||||||||
\(191\) | 16.2448 | 1.17544 | 0.587718 | − | 0.809066i | \(-0.300027\pi\) | ||||
0.587718 | + | 0.809066i | \(0.300027\pi\) | |||||||
\(192\) | 3.26100 | 0.235342 | ||||||||
\(193\) | −18.7181 | −1.34736 | −0.673678 | − | 0.739025i | \(-0.735287\pi\) | ||||
−0.673678 | + | 0.739025i | \(0.735287\pi\) | |||||||
\(194\) | −30.6803 | −2.20271 | ||||||||
\(195\) | −62.0235 | −4.44160 | ||||||||
\(196\) | 49.6941 | 3.54958 | ||||||||
\(197\) | 7.49512 | 0.534005 | 0.267002 | − | 0.963696i | \(-0.413967\pi\) | ||||
0.267002 | + | 0.963696i | \(0.413967\pi\) | |||||||
\(198\) | 53.6803 | 3.81489 | ||||||||
\(199\) | 8.87690 | 0.629266 | 0.314633 | − | 0.949213i | \(-0.398118\pi\) | ||||
0.314633 | + | 0.949213i | \(0.398118\pi\) | |||||||
\(200\) | −37.6959 | −2.66550 | ||||||||
\(201\) | 14.0178 | 0.988741 | ||||||||
\(202\) | −28.3115 | −1.99199 | ||||||||
\(203\) | 41.0630 | 2.88206 | ||||||||
\(204\) | 35.7779 | 2.50496 | ||||||||
\(205\) | −17.9953 | −1.25685 | ||||||||
\(206\) | −12.0215 | −0.837575 | ||||||||
\(207\) | −15.0695 | −1.04740 | ||||||||
\(208\) | 45.3992 | 3.14787 | ||||||||
\(209\) | 31.9578 | 2.21057 | ||||||||
\(210\) | −100.619 | −6.94338 | ||||||||
\(211\) | −10.3385 | −0.711729 | −0.355864 | − | 0.934538i | \(-0.615813\pi\) | ||||
−0.355864 | + | 0.934538i | \(0.615813\pi\) | |||||||
\(212\) | −4.43578 | −0.304650 | ||||||||
\(213\) | 42.7724 | 2.93072 | ||||||||
\(214\) | −44.1402 | −3.01736 | ||||||||
\(215\) | −17.7023 | −1.20728 | ||||||||
\(216\) | 30.7828 | 2.09450 | ||||||||
\(217\) | −37.4468 | −2.54206 | ||||||||
\(218\) | 18.3367 | 1.24192 | ||||||||
\(219\) | 7.50527 | 0.507159 | ||||||||
\(220\) | −65.3486 | −4.40581 | ||||||||
\(221\) | −19.2865 | −1.29735 | ||||||||
\(222\) | −4.35761 | −0.292464 | ||||||||
\(223\) | 7.98377 | 0.534633 | 0.267317 | − | 0.963609i | \(-0.413863\pi\) | ||||
0.267317 | + | 0.963609i | \(0.413863\pi\) | |||||||
\(224\) | 20.9221 | 1.39792 | ||||||||
\(225\) | 29.1926 | 1.94617 | ||||||||
\(226\) | 41.3690 | 2.75182 | ||||||||
\(227\) | −13.1155 | −0.870509 | −0.435255 | − | 0.900307i | \(-0.643342\pi\) | ||||
−0.435255 | + | 0.900307i | \(0.643342\pi\) | |||||||
\(228\) | 89.4516 | 5.92408 | ||||||||
\(229\) | −15.2888 | −1.01031 | −0.505156 | − | 0.863028i | \(-0.668565\pi\) | ||||
−0.505156 | + | 0.863028i | \(0.668565\pi\) | |||||||
\(230\) | 26.6165 | 1.75504 | ||||||||
\(231\) | −52.6393 | −3.46341 | ||||||||
\(232\) | 59.4726 | 3.90457 | ||||||||
\(233\) | −19.3898 | −1.27027 | −0.635134 | − | 0.772402i | \(-0.719055\pi\) | ||||
−0.635134 | + | 0.772402i | \(0.719055\pi\) | |||||||
\(234\) | −80.9962 | −5.29489 | ||||||||
\(235\) | 18.2607 | 1.19120 | ||||||||
\(236\) | −38.7420 | −2.52189 | ||||||||
\(237\) | 2.08450 | 0.135403 | ||||||||
\(238\) | −31.2880 | −2.02810 | ||||||||
\(239\) | 3.16945 | 0.205015 | 0.102507 | − | 0.994732i | \(-0.467313\pi\) | ||||
0.102507 | + | 0.994732i | \(0.467313\pi\) | |||||||
\(240\) | −63.2570 | −4.08322 | ||||||||
\(241\) | −20.0435 | −1.29111 | −0.645557 | − | 0.763712i | \(-0.723375\pi\) | ||||
−0.645557 | + | 0.763712i | \(0.723375\pi\) | |||||||
\(242\) | −21.6960 | −1.39467 | ||||||||
\(243\) | 16.2180 | 1.04039 | ||||||||
\(244\) | −42.8713 | −2.74456 | ||||||||
\(245\) | 37.3253 | 2.38463 | ||||||||
\(246\) | −38.2323 | −2.43760 | ||||||||
\(247\) | −48.2199 | −3.06816 | ||||||||
\(248\) | −54.2352 | −3.44394 | ||||||||
\(249\) | −6.01337 | −0.381082 | ||||||||
\(250\) | −9.30055 | −0.588218 | ||||||||
\(251\) | −10.8561 | −0.685232 | −0.342616 | − | 0.939476i | \(-0.611313\pi\) | ||||
−0.342616 | + | 0.939476i | \(0.611313\pi\) | |||||||
\(252\) | −90.5644 | −5.70502 | ||||||||
\(253\) | 13.9245 | 0.875426 | ||||||||
\(254\) | 20.1200 | 1.26244 | ||||||||
\(255\) | 26.8729 | 1.68285 | ||||||||
\(256\) | −30.0650 | −1.87906 | ||||||||
\(257\) | −1.26039 | −0.0786211 | −0.0393105 | − | 0.999227i | \(-0.512516\pi\) | ||||
−0.0393105 | + | 0.999227i | \(0.512516\pi\) | |||||||
\(258\) | −37.6097 | −2.34148 | ||||||||
\(259\) | 2.62652 | 0.163204 | ||||||||
\(260\) | 98.6021 | 6.11505 | ||||||||
\(261\) | −46.0569 | −2.85085 | ||||||||
\(262\) | 4.38929 | 0.271171 | ||||||||
\(263\) | −9.72372 | −0.599590 | −0.299795 | − | 0.954004i | \(-0.596918\pi\) | ||||
−0.299795 | + | 0.954004i | \(0.596918\pi\) | |||||||
\(264\) | −76.2388 | −4.69217 | ||||||||
\(265\) | −3.33172 | −0.204666 | ||||||||
\(266\) | −78.2259 | −4.79634 | ||||||||
\(267\) | 34.3679 | 2.10328 | ||||||||
\(268\) | −22.2849 | −1.36127 | ||||||||
\(269\) | −1.87130 | −0.114095 | −0.0570476 | − | 0.998371i | \(-0.518169\pi\) | ||||
−0.0570476 | + | 0.998371i | \(0.518169\pi\) | |||||||
\(270\) | 42.1055 | 2.56246 | ||||||||
\(271\) | 0.909353 | 0.0552392 | 0.0276196 | − | 0.999619i | \(-0.491207\pi\) | ||||
0.0276196 | + | 0.999619i | \(0.491207\pi\) | |||||||
\(272\) | −19.6701 | −1.19267 | ||||||||
\(273\) | 79.4254 | 4.80704 | ||||||||
\(274\) | −3.96068 | −0.239274 | ||||||||
\(275\) | −26.9746 | −1.62663 | ||||||||
\(276\) | 38.9754 | 2.34604 | ||||||||
\(277\) | −18.9285 | −1.13730 | −0.568652 | − | 0.822578i | \(-0.692535\pi\) | ||||
−0.568652 | + | 0.822578i | \(0.692535\pi\) | |||||||
\(278\) | 0.622273 | 0.0373214 | ||||||||
\(279\) | 42.0010 | 2.51453 | ||||||||
\(280\) | 87.8372 | 5.24928 | ||||||||
\(281\) | −25.1585 | −1.50083 | −0.750415 | − | 0.660967i | \(-0.770146\pi\) | ||||
−0.750415 | + | 0.660967i | \(0.770146\pi\) | |||||||
\(282\) | 38.7962 | 2.31028 | ||||||||
\(283\) | 11.5483 | 0.686473 | 0.343237 | − | 0.939249i | \(-0.388477\pi\) | ||||
0.343237 | + | 0.939249i | \(0.388477\pi\) | |||||||
\(284\) | −67.9976 | −4.03492 | ||||||||
\(285\) | 67.1873 | 3.97983 | ||||||||
\(286\) | 74.8422 | 4.42551 | ||||||||
\(287\) | 23.0442 | 1.36026 | ||||||||
\(288\) | −23.4666 | −1.38278 | ||||||||
\(289\) | −8.64375 | −0.508456 | ||||||||
\(290\) | 81.3482 | 4.77693 | ||||||||
\(291\) | −33.7442 | −1.97812 | ||||||||
\(292\) | −11.9315 | −0.698240 | ||||||||
\(293\) | 1.59756 | 0.0933307 | 0.0466653 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466653 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(294\) | 79.3004 | 4.62489 | ||||||||
\(295\) | −29.0992 | −1.69422 | ||||||||
\(296\) | 3.80405 | 0.221106 | ||||||||
\(297\) | 22.0276 | 1.27817 | ||||||||
\(298\) | −37.9028 | −2.19565 | ||||||||
\(299\) | −21.0102 | −1.21505 | ||||||||
\(300\) | −75.5033 | −4.35918 | ||||||||
\(301\) | 22.6690 | 1.30662 | ||||||||
\(302\) | −2.53688 | −0.145981 | ||||||||
\(303\) | −31.1388 | −1.78888 | ||||||||
\(304\) | −49.1789 | −2.82060 | ||||||||
\(305\) | −32.2008 | −1.84381 | ||||||||
\(306\) | 35.0931 | 2.00614 | ||||||||
\(307\) | 2.22523 | 0.127000 | 0.0635002 | − | 0.997982i | \(-0.479774\pi\) | ||||
0.0635002 | + | 0.997982i | \(0.479774\pi\) | |||||||
\(308\) | 83.6835 | 4.76831 | ||||||||
\(309\) | −13.2220 | −0.752172 | ||||||||
\(310\) | −74.1844 | −4.21339 | ||||||||
\(311\) | −30.8442 | −1.74902 | −0.874508 | − | 0.485010i | \(-0.838816\pi\) | ||||
−0.874508 | + | 0.485010i | \(0.838816\pi\) | |||||||
\(312\) | 115.034 | 6.51251 | ||||||||
\(313\) | −26.0160 | −1.47051 | −0.735256 | − | 0.677789i | \(-0.762938\pi\) | ||||
−0.735256 | + | 0.677789i | \(0.762938\pi\) | |||||||
\(314\) | −3.61174 | −0.203822 | ||||||||
\(315\) | −68.0231 | −3.83267 | ||||||||
\(316\) | −3.31384 | −0.186418 | ||||||||
\(317\) | −13.6480 | −0.766548 | −0.383274 | − | 0.923635i | \(-0.625204\pi\) | ||||
−0.383274 | + | 0.923635i | \(0.625204\pi\) | |||||||
\(318\) | −7.07848 | −0.396942 | ||||||||
\(319\) | 42.5576 | 2.38277 | ||||||||
\(320\) | −3.89385 | −0.217673 | ||||||||
\(321\) | −48.5482 | −2.70970 | ||||||||
\(322\) | −34.0842 | −1.89944 | ||||||||
\(323\) | 20.8922 | 1.16247 | ||||||||
\(324\) | −2.02404 | −0.112447 | ||||||||
\(325\) | 40.7009 | 2.25768 | ||||||||
\(326\) | −42.6156 | −2.36026 | ||||||||
\(327\) | 20.1679 | 1.11529 | ||||||||
\(328\) | 33.3755 | 1.84285 | ||||||||
\(329\) | −23.3841 | −1.28921 | ||||||||
\(330\) | −104.281 | −5.74051 | ||||||||
\(331\) | 4.00337 | 0.220045 | 0.110023 | − | 0.993929i | \(-0.464908\pi\) | ||||
0.110023 | + | 0.993929i | \(0.464908\pi\) | |||||||
\(332\) | 9.55978 | 0.524661 | ||||||||
\(333\) | −2.94594 | −0.161437 | ||||||||
\(334\) | −5.30771 | −0.290425 | ||||||||
\(335\) | −16.7382 | −0.914507 | ||||||||
\(336\) | 81.0049 | 4.41918 | ||||||||
\(337\) | 15.2092 | 0.828496 | 0.414248 | − | 0.910164i | \(-0.364045\pi\) | ||||
0.414248 | + | 0.910164i | \(0.364045\pi\) | |||||||
\(338\) | −79.9472 | −4.34855 | ||||||||
\(339\) | 45.5003 | 2.47124 | ||||||||
\(340\) | −42.7213 | −2.31689 | ||||||||
\(341\) | −38.8098 | −2.10167 | ||||||||
\(342\) | 87.7395 | 4.74441 | ||||||||
\(343\) | −17.9322 | −0.968247 | ||||||||
\(344\) | 32.8321 | 1.77019 | ||||||||
\(345\) | 29.2745 | 1.57609 | ||||||||
\(346\) | 21.4026 | 1.15061 | ||||||||
\(347\) | 24.8818 | 1.33572 | 0.667862 | − | 0.744285i | \(-0.267210\pi\) | ||||
0.667862 | + | 0.744285i | \(0.267210\pi\) | |||||||
\(348\) | 119.121 | 6.38556 | ||||||||
\(349\) | −10.4576 | −0.559784 | −0.279892 | − | 0.960032i | \(-0.590299\pi\) | ||||
−0.279892 | + | 0.960032i | \(0.590299\pi\) | |||||||
\(350\) | 66.0281 | 3.52935 | ||||||||
\(351\) | −33.2367 | −1.77404 | ||||||||
\(352\) | 21.6836 | 1.15574 | ||||||||
\(353\) | 10.6149 | 0.564977 | 0.282488 | − | 0.959271i | \(-0.408840\pi\) | ||||
0.282488 | + | 0.959271i | \(0.408840\pi\) | |||||||
\(354\) | −61.8233 | −3.28587 | ||||||||
\(355\) | −51.0732 | −2.71068 | ||||||||
\(356\) | −54.6365 | −2.89573 | ||||||||
\(357\) | −34.4126 | −1.82131 | ||||||||
\(358\) | 3.13421 | 0.165648 | ||||||||
\(359\) | 18.3411 | 0.968006 | 0.484003 | − | 0.875066i | \(-0.339182\pi\) | ||||
0.484003 | + | 0.875066i | \(0.339182\pi\) | |||||||
\(360\) | −98.5196 | −5.19244 | ||||||||
\(361\) | 33.2345 | 1.74918 | ||||||||
\(362\) | −29.2883 | −1.53936 | ||||||||
\(363\) | −23.8627 | −1.25247 | ||||||||
\(364\) | −126.267 | −6.61818 | ||||||||
\(365\) | −8.96180 | −0.469082 | ||||||||
\(366\) | −68.4129 | −3.57600 | ||||||||
\(367\) | −31.9156 | −1.66598 | −0.832991 | − | 0.553286i | \(-0.813373\pi\) | ||||
−0.832991 | + | 0.553286i | \(0.813373\pi\) | |||||||
\(368\) | −21.4280 | −1.11701 | ||||||||
\(369\) | −25.8468 | −1.34553 | ||||||||
\(370\) | 5.20329 | 0.270506 | ||||||||
\(371\) | 4.26650 | 0.221506 | ||||||||
\(372\) | −108.631 | −5.63224 | ||||||||
\(373\) | 1.91673 | 0.0992448 | 0.0496224 | − | 0.998768i | \(-0.484198\pi\) | ||||
0.0496224 | + | 0.998768i | \(0.484198\pi\) | |||||||
\(374\) | −32.4268 | −1.67675 | ||||||||
\(375\) | −10.2293 | −0.528241 | ||||||||
\(376\) | −33.8678 | −1.74660 | ||||||||
\(377\) | −64.2136 | −3.30717 | ||||||||
\(378\) | −53.9190 | −2.77329 | ||||||||
\(379\) | −31.9891 | −1.64317 | −0.821585 | − | 0.570086i | \(-0.806910\pi\) | ||||
−0.821585 | + | 0.570086i | \(0.806910\pi\) | |||||||
\(380\) | −106.811 | −5.47930 | ||||||||
\(381\) | 22.1293 | 1.13372 | ||||||||
\(382\) | −41.2113 | −2.10855 | ||||||||
\(383\) | 27.4791 | 1.40412 | 0.702058 | − | 0.712120i | \(-0.252265\pi\) | ||||
0.702058 | + | 0.712120i | \(0.252265\pi\) | |||||||
\(384\) | −35.6383 | −1.81866 | ||||||||
\(385\) | 62.8548 | 3.20338 | ||||||||
\(386\) | 47.4856 | 2.41695 | ||||||||
\(387\) | −25.4259 | −1.29247 | ||||||||
\(388\) | 53.6449 | 2.72341 | ||||||||
\(389\) | 32.4682 | 1.64620 | 0.823102 | − | 0.567893i | \(-0.192241\pi\) | ||||
0.823102 | + | 0.567893i | \(0.192241\pi\) | |||||||
\(390\) | 157.346 | 7.96755 | ||||||||
\(391\) | 9.10305 | 0.460361 | ||||||||
\(392\) | −69.2266 | −3.49647 | ||||||||
\(393\) | 4.82763 | 0.243522 | ||||||||
\(394\) | −19.0142 | −0.957923 | ||||||||
\(395\) | −2.48904 | −0.125237 | ||||||||
\(396\) | −93.8607 | −4.71668 | ||||||||
\(397\) | 24.3180 | 1.22049 | 0.610244 | − | 0.792214i | \(-0.291071\pi\) | ||||
0.610244 | + | 0.792214i | \(0.291071\pi\) | |||||||
\(398\) | −22.5196 | −1.12881 | ||||||||
\(399\) | −86.0380 | −4.30729 | ||||||||
\(400\) | 41.5103 | 2.07552 | ||||||||
\(401\) | 17.7472 | 0.886253 | 0.443127 | − | 0.896459i | \(-0.353869\pi\) | ||||
0.443127 | + | 0.896459i | \(0.353869\pi\) | |||||||
\(402\) | −35.5616 | −1.77365 | ||||||||
\(403\) | 58.5587 | 2.91702 | ||||||||
\(404\) | 49.5030 | 2.46287 | ||||||||
\(405\) | −1.52026 | −0.0755424 | ||||||||
\(406\) | −104.172 | −5.16997 | ||||||||
\(407\) | 2.72212 | 0.134930 | ||||||||
\(408\) | −49.8406 | −2.46748 | ||||||||
\(409\) | −4.29402 | −0.212325 | −0.106163 | − | 0.994349i | \(-0.533856\pi\) | ||||
−0.106163 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(410\) | 45.6520 | 2.25459 | ||||||||
\(411\) | −4.35621 | −0.214876 | ||||||||
\(412\) | 21.0197 | 1.03557 | ||||||||
\(413\) | 37.2635 | 1.83362 | ||||||||
\(414\) | 38.2294 | 1.87887 | ||||||||
\(415\) | 7.18037 | 0.352471 | ||||||||
\(416\) | −32.7176 | −1.60411 | ||||||||
\(417\) | 0.684416 | 0.0335160 | ||||||||
\(418\) | −81.0732 | −3.96542 | ||||||||
\(419\) | −12.3248 | −0.602108 | −0.301054 | − | 0.953607i | \(-0.597338\pi\) | ||||
−0.301054 | + | 0.953607i | \(0.597338\pi\) | |||||||
\(420\) | 175.934 | 8.58470 | ||||||||
\(421\) | 23.5935 | 1.14988 | 0.574939 | − | 0.818196i | \(-0.305026\pi\) | ||||
0.574939 | + | 0.818196i | \(0.305026\pi\) | |||||||
\(422\) | 26.2274 | 1.27673 | ||||||||
\(423\) | 26.2280 | 1.27525 | ||||||||
\(424\) | 6.17928 | 0.300092 | ||||||||
\(425\) | −17.6345 | −0.855397 | ||||||||
\(426\) | −108.509 | −5.25726 | ||||||||
\(427\) | 41.2353 | 1.99552 | ||||||||
\(428\) | 77.1797 | 3.73062 | ||||||||
\(429\) | 82.3163 | 3.97427 | ||||||||
\(430\) | 44.9086 | 2.16568 | ||||||||
\(431\) | −8.18146 | −0.394087 | −0.197044 | − | 0.980395i | \(-0.563134\pi\) | ||||
−0.197044 | + | 0.980395i | \(0.563134\pi\) | |||||||
\(432\) | −33.8977 | −1.63090 | ||||||||
\(433\) | 11.8709 | 0.570477 | 0.285239 | − | 0.958457i | \(-0.407927\pi\) | ||||
0.285239 | + | 0.958457i | \(0.407927\pi\) | |||||||
\(434\) | 94.9982 | 4.56006 | ||||||||
\(435\) | 89.4721 | 4.28986 | ||||||||
\(436\) | −32.0621 | −1.53549 | ||||||||
\(437\) | 22.7594 | 1.08873 | ||||||||
\(438\) | −19.0400 | −0.909766 | ||||||||
\(439\) | 38.5659 | 1.84065 | 0.920325 | − | 0.391154i | \(-0.127924\pi\) | ||||
0.920325 | + | 0.391154i | \(0.127924\pi\) | |||||||
\(440\) | 91.0343 | 4.33989 | ||||||||
\(441\) | 53.6107 | 2.55289 | ||||||||
\(442\) | 48.9276 | 2.32725 | ||||||||
\(443\) | 2.39972 | 0.114014 | 0.0570071 | − | 0.998374i | \(-0.481844\pi\) | ||||
0.0570071 | + | 0.998374i | \(0.481844\pi\) | |||||||
\(444\) | 7.61935 | 0.361598 | ||||||||
\(445\) | −41.0376 | −1.94537 | ||||||||
\(446\) | −20.2539 | −0.959050 | ||||||||
\(447\) | −41.6880 | −1.97177 | ||||||||
\(448\) | 4.98635 | 0.235583 | ||||||||
\(449\) | −6.43202 | −0.303546 | −0.151773 | − | 0.988415i | \(-0.548498\pi\) | ||||
−0.151773 | + | 0.988415i | \(0.548498\pi\) | |||||||
\(450\) | −74.0582 | −3.49114 | ||||||||
\(451\) | 23.8830 | 1.12461 | ||||||||
\(452\) | −72.3342 | −3.40232 | ||||||||
\(453\) | −2.79023 | −0.131096 | ||||||||
\(454\) | 33.2726 | 1.56156 | ||||||||
\(455\) | −94.8393 | −4.44614 | ||||||||
\(456\) | −124.611 | −5.83544 | ||||||||
\(457\) | −13.4364 | −0.628531 | −0.314265 | − | 0.949335i | \(-0.601758\pi\) | ||||
−0.314265 | + | 0.949335i | \(0.601758\pi\) | |||||||
\(458\) | 38.7859 | 1.81235 | ||||||||
\(459\) | 14.4004 | 0.672154 | ||||||||
\(460\) | −46.5393 | −2.16991 | ||||||||
\(461\) | −35.2743 | −1.64289 | −0.821444 | − | 0.570289i | \(-0.806831\pi\) | ||||
−0.821444 | + | 0.570289i | \(0.806831\pi\) | |||||||
\(462\) | 133.540 | 6.21283 | ||||||||
\(463\) | 2.76050 | 0.128291 | 0.0641457 | − | 0.997941i | \(-0.479568\pi\) | ||||
0.0641457 | + | 0.997941i | \(0.479568\pi\) | |||||||
\(464\) | −65.4906 | −3.04032 | ||||||||
\(465\) | −81.5928 | −3.78378 | ||||||||
\(466\) | 49.1897 | 2.27867 | ||||||||
\(467\) | −35.8710 | −1.65991 | −0.829956 | − | 0.557829i | \(-0.811635\pi\) | ||||
−0.829956 | + | 0.557829i | \(0.811635\pi\) | |||||||
\(468\) | 141.623 | 6.54652 | ||||||||
\(469\) | 21.4345 | 0.989752 | ||||||||
\(470\) | −46.3253 | −2.13682 | ||||||||
\(471\) | −3.97243 | −0.183040 | ||||||||
\(472\) | 53.9697 | 2.48416 | ||||||||
\(473\) | 23.4941 | 1.08026 | ||||||||
\(474\) | −5.28814 | −0.242892 | ||||||||
\(475\) | −44.0895 | −2.02296 | ||||||||
\(476\) | 54.7075 | 2.50752 | ||||||||
\(477\) | −4.78538 | −0.219107 | ||||||||
\(478\) | −8.04053 | −0.367765 | ||||||||
\(479\) | −7.79711 | −0.356259 | −0.178129 | − | 0.984007i | \(-0.557005\pi\) | ||||
−0.178129 | + | 0.984007i | \(0.557005\pi\) | |||||||
\(480\) | 45.5871 | 2.08076 | ||||||||
\(481\) | −4.10730 | −0.187277 | ||||||||
\(482\) | 50.8480 | 2.31606 | ||||||||
\(483\) | −37.4881 | −1.70577 | ||||||||
\(484\) | 37.9358 | 1.72435 | ||||||||
\(485\) | 40.2928 | 1.82960 | ||||||||
\(486\) | −41.1432 | −1.86629 | ||||||||
\(487\) | 22.3134 | 1.01112 | 0.505558 | − | 0.862793i | \(-0.331287\pi\) | ||||
0.505558 | + | 0.862793i | \(0.331287\pi\) | |||||||
\(488\) | 59.7221 | 2.70349 | ||||||||
\(489\) | −46.8714 | −2.11960 | ||||||||
\(490\) | −94.6900 | −4.27766 | ||||||||
\(491\) | 0.762988 | 0.0344332 | 0.0172166 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172166 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(492\) | 66.8497 | 3.01382 | ||||||||
\(493\) | 27.8218 | 1.25303 | ||||||||
\(494\) | 122.328 | 5.50381 | ||||||||
\(495\) | −70.4990 | −3.16870 | ||||||||
\(496\) | 59.7232 | 2.68165 | ||||||||
\(497\) | 65.4027 | 2.93371 | ||||||||
\(498\) | 15.2552 | 0.683603 | ||||||||
\(499\) | −4.25179 | −0.190336 | −0.0951682 | − | 0.995461i | \(-0.530339\pi\) | ||||
−0.0951682 | + | 0.995461i | \(0.530339\pi\) | |||||||
\(500\) | 16.2621 | 0.727265 | ||||||||
\(501\) | −5.83776 | −0.260812 | ||||||||
\(502\) | 27.5407 | 1.22920 | ||||||||
\(503\) | −31.9438 | −1.42430 | −0.712152 | − | 0.702026i | \(-0.752279\pi\) | ||||
−0.712152 | + | 0.702026i | \(0.752279\pi\) | |||||||
\(504\) | 126.161 | 5.61967 | ||||||||
\(505\) | 37.1818 | 1.65457 | ||||||||
\(506\) | −35.3248 | −1.57038 | ||||||||
\(507\) | −87.9311 | −3.90516 | ||||||||
\(508\) | −35.1802 | −1.56087 | ||||||||
\(509\) | 27.2916 | 1.20968 | 0.604839 | − | 0.796348i | \(-0.293237\pi\) | ||||
0.604839 | + | 0.796348i | \(0.293237\pi\) | |||||||
\(510\) | −68.1734 | −3.01877 | ||||||||
\(511\) | 11.4762 | 0.507677 | ||||||||
\(512\) | 50.7263 | 2.24181 | ||||||||
\(513\) | 36.0038 | 1.58961 | ||||||||
\(514\) | 3.19747 | 0.141034 | ||||||||
\(515\) | 15.7879 | 0.695700 | ||||||||
\(516\) | 65.7612 | 2.89497 | ||||||||
\(517\) | −24.2352 | −1.06586 | ||||||||
\(518\) | −6.66317 | −0.292763 | ||||||||
\(519\) | 23.5400 | 1.03329 | ||||||||
\(520\) | −137.358 | −6.02356 | ||||||||
\(521\) | −29.1086 | −1.27527 | −0.637636 | − | 0.770338i | \(-0.720088\pi\) | ||||
−0.637636 | + | 0.770338i | \(0.720088\pi\) | |||||||
\(522\) | 116.841 | 5.11399 | ||||||||
\(523\) | −18.0367 | −0.788688 | −0.394344 | − | 0.918963i | \(-0.629028\pi\) | ||||
−0.394344 | + | 0.918963i | \(0.629028\pi\) | |||||||
\(524\) | −7.67474 | −0.335273 | ||||||||
\(525\) | 72.6219 | 3.16948 | ||||||||
\(526\) | 24.6679 | 1.07557 | ||||||||
\(527\) | −25.3717 | −1.10521 | ||||||||
\(528\) | 83.9534 | 3.65360 | ||||||||
\(529\) | −13.0834 | −0.568844 | ||||||||
\(530\) | 8.45219 | 0.367140 | ||||||||
\(531\) | −41.7954 | −1.81376 | ||||||||
\(532\) | 136.779 | 5.93013 | ||||||||
\(533\) | −36.0361 | −1.56090 | ||||||||
\(534\) | −87.1874 | −3.77297 | ||||||||
\(535\) | 57.9699 | 2.50626 | ||||||||
\(536\) | 31.0441 | 1.34090 | ||||||||
\(537\) | 3.44720 | 0.148758 | ||||||||
\(538\) | 4.74727 | 0.204669 | ||||||||
\(539\) | −49.5374 | −2.13373 | ||||||||
\(540\) | −73.6221 | −3.16819 | ||||||||
\(541\) | −15.7832 | −0.678572 | −0.339286 | − | 0.940683i | \(-0.610185\pi\) | ||||
−0.339286 | + | 0.940683i | \(0.610185\pi\) | |||||||
\(542\) | −2.30692 | −0.0990908 | ||||||||
\(543\) | −32.2132 | −1.38240 | ||||||||
\(544\) | 14.1755 | 0.607771 | ||||||||
\(545\) | −24.0819 | −1.03155 | ||||||||
\(546\) | −201.493 | −8.62310 | ||||||||
\(547\) | 13.5489 | 0.579309 | 0.289655 | − | 0.957131i | \(-0.406460\pi\) | ||||
0.289655 | + | 0.957131i | \(0.406460\pi\) | |||||||
\(548\) | 6.92531 | 0.295835 | ||||||||
\(549\) | −46.2502 | −1.97391 | ||||||||
\(550\) | 68.4313 | 2.91792 | ||||||||
\(551\) | 69.5597 | 2.96334 | ||||||||
\(552\) | −54.2949 | −2.31094 | ||||||||
\(553\) | 3.18738 | 0.135541 | ||||||||
\(554\) | 48.0194 | 2.04015 | ||||||||
\(555\) | 5.72291 | 0.242924 | ||||||||
\(556\) | −1.08805 | −0.0461437 | ||||||||
\(557\) | −36.3645 | −1.54081 | −0.770407 | − | 0.637552i | \(-0.779947\pi\) | ||||
−0.770407 | + | 0.637552i | \(0.779947\pi\) | |||||||
\(558\) | −106.552 | −4.51069 | ||||||||
\(559\) | −35.4493 | −1.49935 | ||||||||
\(560\) | −96.7254 | −4.08739 | ||||||||
\(561\) | −35.6651 | −1.50578 | ||||||||
\(562\) | 63.8242 | 2.69226 | ||||||||
\(563\) | 35.1359 | 1.48080 | 0.740400 | − | 0.672166i | \(-0.234636\pi\) | ||||
0.740400 | + | 0.672166i | \(0.234636\pi\) | |||||||
\(564\) | −67.8357 | −2.85640 | ||||||||
\(565\) | −54.3304 | −2.28570 | ||||||||
\(566\) | −29.2966 | −1.23143 | ||||||||
\(567\) | 1.94680 | 0.0817579 | ||||||||
\(568\) | 94.7244 | 3.97455 | ||||||||
\(569\) | 13.5574 | 0.568355 | 0.284178 | − | 0.958772i | \(-0.408279\pi\) | ||||
0.284178 | + | 0.958772i | \(0.408279\pi\) | |||||||
\(570\) | −170.446 | −7.13921 | ||||||||
\(571\) | 21.6231 | 0.904900 | 0.452450 | − | 0.891790i | \(-0.350550\pi\) | ||||
0.452450 | + | 0.891790i | \(0.350550\pi\) | |||||||
\(572\) | −130.863 | −5.47164 | ||||||||
\(573\) | −45.3268 | −1.89356 | ||||||||
\(574\) | −58.4605 | −2.44009 | ||||||||
\(575\) | −19.2105 | −0.801131 | ||||||||
\(576\) | −5.59277 | −0.233032 | ||||||||
\(577\) | −10.9765 | −0.456959 | −0.228479 | − | 0.973549i | \(-0.573375\pi\) | ||||
−0.228479 | + | 0.973549i | \(0.573375\pi\) | |||||||
\(578\) | 21.9282 | 0.912092 | ||||||||
\(579\) | 52.2277 | 2.17051 | ||||||||
\(580\) | −142.239 | −5.90613 | ||||||||
\(581\) | −9.19496 | −0.381471 | ||||||||
\(582\) | 85.6050 | 3.54844 | ||||||||
\(583\) | 4.42179 | 0.183132 | ||||||||
\(584\) | 16.6213 | 0.687793 | ||||||||
\(585\) | 106.373 | 4.39800 | ||||||||
\(586\) | −4.05283 | −0.167421 | ||||||||
\(587\) | 1.19047 | 0.0491361 | 0.0245681 | − | 0.999698i | \(-0.492179\pi\) | ||||
0.0245681 | + | 0.999698i | \(0.492179\pi\) | |||||||
\(588\) | −138.658 | −5.71815 | ||||||||
\(589\) | −63.4340 | −2.61375 | ||||||||
\(590\) | 73.8212 | 3.03917 | ||||||||
\(591\) | −20.9131 | −0.860250 | ||||||||
\(592\) | −4.18898 | −0.172166 | ||||||||
\(593\) | −28.8636 | −1.18529 | −0.592643 | − | 0.805465i | \(-0.701915\pi\) | ||||
−0.592643 | + | 0.805465i | \(0.701915\pi\) | |||||||
\(594\) | −55.8815 | −2.29285 | ||||||||
\(595\) | 41.0910 | 1.68456 | ||||||||
\(596\) | 66.2736 | 2.71467 | ||||||||
\(597\) | −24.7686 | −1.01371 | ||||||||
\(598\) | 53.3003 | 2.17961 | ||||||||
\(599\) | 45.0409 | 1.84032 | 0.920161 | − | 0.391540i | \(-0.128058\pi\) | ||||
0.920161 | + | 0.391540i | \(0.128058\pi\) | |||||||
\(600\) | 105.180 | 4.29396 | ||||||||
\(601\) | −4.05588 | −0.165443 | −0.0827215 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827215 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(602\) | −57.5085 | −2.34387 | ||||||||
\(603\) | −24.0413 | −0.979035 | ||||||||
\(604\) | 4.43578 | 0.180489 | ||||||||
\(605\) | 28.4937 | 1.15843 | ||||||||
\(606\) | 78.9954 | 3.20897 | ||||||||
\(607\) | −20.2712 | −0.822783 | −0.411392 | − | 0.911459i | \(-0.634957\pi\) | ||||
−0.411392 | + | 0.911459i | \(0.634957\pi\) | |||||||
\(608\) | 35.4415 | 1.43734 | ||||||||
\(609\) | −114.575 | −4.64282 | ||||||||
\(610\) | 81.6896 | 3.30751 | ||||||||
\(611\) | 36.5676 | 1.47937 | ||||||||
\(612\) | −61.3609 | −2.48037 | ||||||||
\(613\) | 23.9420 | 0.967009 | 0.483504 | − | 0.875342i | \(-0.339364\pi\) | ||||
0.483504 | + | 0.875342i | \(0.339364\pi\) | |||||||
\(614\) | −5.64514 | −0.227819 | ||||||||
\(615\) | 50.2110 | 2.02470 | ||||||||
\(616\) | −116.576 | −4.69697 | ||||||||
\(617\) | −2.09864 | −0.0844881 | −0.0422441 | − | 0.999107i | \(-0.513451\pi\) | ||||
−0.0422441 | + | 0.999107i | \(0.513451\pi\) | |||||||
\(618\) | 33.5426 | 1.34928 | ||||||||
\(619\) | −30.8519 | −1.24004 | −0.620022 | − | 0.784584i | \(-0.712876\pi\) | ||||
−0.620022 | + | 0.784584i | \(0.712876\pi\) | |||||||
\(620\) | 129.712 | 5.20938 | ||||||||
\(621\) | 15.6874 | 0.629514 | ||||||||
\(622\) | 78.2483 | 3.13747 | ||||||||
\(623\) | 52.5515 | 2.10543 | ||||||||
\(624\) | −126.674 | −5.07102 | ||||||||
\(625\) | −18.2873 | −0.731493 | ||||||||
\(626\) | 65.9996 | 2.63788 | ||||||||
\(627\) | −89.1696 | −3.56109 | ||||||||
\(628\) | 6.31518 | 0.252003 | ||||||||
\(629\) | 1.77957 | 0.0709559 | ||||||||
\(630\) | 172.567 | 6.87522 | ||||||||
\(631\) | 21.0748 | 0.838976 | 0.419488 | − | 0.907761i | \(-0.362210\pi\) | ||||
0.419488 | + | 0.907761i | \(0.362210\pi\) | |||||||
\(632\) | 4.61637 | 0.183629 | ||||||||
\(633\) | 28.8467 | 1.14655 | ||||||||
\(634\) | 34.6234 | 1.37507 | ||||||||
\(635\) | −26.4239 | −1.04860 | ||||||||
\(636\) | 12.3768 | 0.490773 | ||||||||
\(637\) | 74.7452 | 2.96151 | ||||||||
\(638\) | −107.964 | −4.27432 | ||||||||
\(639\) | −73.3568 | −2.90195 | ||||||||
\(640\) | 42.5545 | 1.68212 | ||||||||
\(641\) | 10.2635 | 0.405386 | 0.202693 | − | 0.979242i | \(-0.435031\pi\) | ||||
0.202693 | + | 0.979242i | \(0.435031\pi\) | |||||||
\(642\) | 123.161 | 4.86079 | ||||||||
\(643\) | −15.6338 | −0.616538 | −0.308269 | − | 0.951299i | \(-0.599750\pi\) | ||||
−0.308269 | + | 0.951299i | \(0.599750\pi\) | |||||||
\(644\) | 59.5968 | 2.34844 | ||||||||
\(645\) | 49.3934 | 1.94486 | ||||||||
\(646\) | −53.0011 | −2.08530 | ||||||||
\(647\) | 23.3802 | 0.919170 | 0.459585 | − | 0.888134i | \(-0.347998\pi\) | ||||
0.459585 | + | 0.888134i | \(0.347998\pi\) | |||||||
\(648\) | 2.81960 | 0.110764 | ||||||||
\(649\) | 38.6198 | 1.51596 | ||||||||
\(650\) | −103.253 | −4.04993 | ||||||||
\(651\) | 104.485 | 4.09510 | ||||||||
\(652\) | 74.5139 | 2.91819 | ||||||||
\(653\) | −3.16171 | −0.123727 | −0.0618637 | − | 0.998085i | \(-0.519704\pi\) | ||||
−0.0618637 | + | 0.998085i | \(0.519704\pi\) | |||||||
\(654\) | −51.1637 | −2.00066 | ||||||||
\(655\) | −5.76452 | −0.225238 | ||||||||
\(656\) | −36.7528 | −1.43495 | ||||||||
\(657\) | −12.8719 | −0.502181 | ||||||||
\(658\) | 59.3227 | 2.31264 | ||||||||
\(659\) | −42.7875 | −1.66676 | −0.833382 | − | 0.552698i | \(-0.813598\pi\) | ||||
−0.833382 | + | 0.552698i | \(0.813598\pi\) | |||||||
\(660\) | 182.338 | 7.09748 | ||||||||
\(661\) | 34.9870 | 1.36084 | 0.680418 | − | 0.732824i | \(-0.261798\pi\) | ||||
0.680418 | + | 0.732824i | \(0.261798\pi\) | |||||||
\(662\) | −10.1561 | −0.394727 | ||||||||
\(663\) | 53.8138 | 2.08995 | ||||||||
\(664\) | −13.3173 | −0.516811 | ||||||||
\(665\) | 102.735 | 3.98390 | ||||||||
\(666\) | 7.47352 | 0.289593 | ||||||||
\(667\) | 30.3082 | 1.17354 | ||||||||
\(668\) | 9.28060 | 0.359077 | ||||||||
\(669\) | −22.2766 | −0.861261 | ||||||||
\(670\) | 42.4629 | 1.64049 | ||||||||
\(671\) | 42.7362 | 1.64981 | ||||||||
\(672\) | −58.3775 | −2.25196 | ||||||||
\(673\) | −4.83381 | −0.186330 | −0.0931648 | − | 0.995651i | \(-0.529698\pi\) | ||||
−0.0931648 | + | 0.995651i | \(0.529698\pi\) | |||||||
\(674\) | −38.5839 | −1.48620 | ||||||||
\(675\) | −30.3897 | −1.16970 | ||||||||
\(676\) | 139.789 | 5.37649 | ||||||||
\(677\) | −26.0103 | −0.999657 | −0.499828 | − | 0.866124i | \(-0.666604\pi\) | ||||
−0.499828 | + | 0.866124i | \(0.666604\pi\) | |||||||
\(678\) | −115.429 | −4.43302 | ||||||||
\(679\) | −51.5977 | −1.98014 | ||||||||
\(680\) | 59.5131 | 2.28222 | ||||||||
\(681\) | 36.5954 | 1.40234 | ||||||||
\(682\) | 98.4560 | 3.77007 | ||||||||
\(683\) | −3.43112 | −0.131288 | −0.0656440 | − | 0.997843i | \(-0.520910\pi\) | ||||
−0.0656440 | + | 0.997843i | \(0.520910\pi\) | |||||||
\(684\) | −153.414 | −5.86592 | ||||||||
\(685\) | 5.20162 | 0.198744 | ||||||||
\(686\) | 45.4919 | 1.73689 | ||||||||
\(687\) | 42.6593 | 1.62755 | ||||||||
\(688\) | −36.1543 | −1.37837 | ||||||||
\(689\) | −6.67188 | −0.254178 | ||||||||
\(690\) | −74.2661 | −2.82726 | ||||||||
\(691\) | 3.54444 | 0.134837 | 0.0674185 | − | 0.997725i | \(-0.478524\pi\) | ||||
0.0674185 | + | 0.997725i | \(0.478524\pi\) | |||||||
\(692\) | −37.4228 | −1.42260 | ||||||||
\(693\) | 90.2789 | 3.42941 | ||||||||
\(694\) | −63.1222 | −2.39609 | ||||||||
\(695\) | −0.817239 | −0.0309996 | ||||||||
\(696\) | −165.942 | −6.29002 | ||||||||
\(697\) | 15.6133 | 0.591397 | ||||||||
\(698\) | 26.5298 | 1.00417 | ||||||||
\(699\) | 54.1020 | 2.04633 | ||||||||
\(700\) | −115.451 | −4.36364 | ||||||||
\(701\) | 14.3919 | 0.543576 | 0.271788 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271788 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(702\) | 84.3176 | 3.18236 | ||||||||
\(703\) | 4.44925 | 0.167807 | ||||||||
\(704\) | 5.16784 | 0.194770 | ||||||||
\(705\) | −50.9515 | −1.91895 | ||||||||
\(706\) | −26.9289 | −1.01348 | ||||||||
\(707\) | −47.6139 | −1.79070 | ||||||||
\(708\) | 108.099 | 4.06261 | ||||||||
\(709\) | −11.6729 | −0.438385 | −0.219193 | − | 0.975682i | \(-0.570342\pi\) | ||||
−0.219193 | + | 0.975682i | \(0.570342\pi\) | |||||||
\(710\) | 129.567 | 4.86255 | ||||||||
\(711\) | −3.57502 | −0.134074 | ||||||||
\(712\) | 76.1117 | 2.85241 | ||||||||
\(713\) | −27.6391 | −1.03509 | ||||||||
\(714\) | 87.3007 | 3.26715 | ||||||||
\(715\) | −98.2913 | −3.67588 | ||||||||
\(716\) | −5.48020 | −0.204805 | ||||||||
\(717\) | −8.84349 | −0.330266 | ||||||||
\(718\) | −46.5292 | −1.73645 | ||||||||
\(719\) | −15.3409 | −0.572118 | −0.286059 | − | 0.958212i | \(-0.592345\pi\) | ||||
−0.286059 | + | 0.958212i | \(0.592345\pi\) | |||||||
\(720\) | 108.489 | 4.04314 | ||||||||
\(721\) | −20.2175 | −0.752941 | ||||||||
\(722\) | −84.3120 | −3.13777 | ||||||||
\(723\) | 55.9259 | 2.07991 | ||||||||
\(724\) | 51.2110 | 1.90324 | ||||||||
\(725\) | −58.7131 | −2.18055 | ||||||||
\(726\) | 60.5369 | 2.24673 | ||||||||
\(727\) | 12.0691 | 0.447618 | 0.223809 | − | 0.974633i | \(-0.428151\pi\) | ||||
0.223809 | + | 0.974633i | \(0.428151\pi\) | |||||||
\(728\) | 175.897 | 6.51916 | ||||||||
\(729\) | −43.8831 | −1.62530 | ||||||||
\(730\) | 22.7350 | 0.841462 | ||||||||
\(731\) | 15.3591 | 0.568077 | ||||||||
\(732\) | 119.621 | 4.42131 | ||||||||
\(733\) | 49.0519 | 1.81177 | 0.905886 | − | 0.423522i | \(-0.139206\pi\) | ||||
0.905886 | + | 0.423522i | \(0.139206\pi\) | |||||||
\(734\) | 80.9662 | 2.98852 | ||||||||
\(735\) | −104.146 | −3.84149 | ||||||||
\(736\) | 15.4424 | 0.569215 | ||||||||
\(737\) | 22.2146 | 0.818286 | ||||||||
\(738\) | 65.5702 | 2.41367 | ||||||||
\(739\) | 11.7857 | 0.433543 | 0.216772 | − | 0.976222i | \(-0.430447\pi\) | ||||
0.216772 | + | 0.976222i | \(0.430447\pi\) | |||||||
\(740\) | −9.09802 | −0.334450 | ||||||||
\(741\) | 134.545 | 4.94262 | ||||||||
\(742\) | −10.8236 | −0.397347 | ||||||||
\(743\) | 26.9068 | 0.987116 | 0.493558 | − | 0.869713i | \(-0.335696\pi\) | ||||
0.493558 | + | 0.869713i | \(0.335696\pi\) | |||||||
\(744\) | 151.329 | 5.54798 | ||||||||
\(745\) | 49.7783 | 1.82373 | ||||||||
\(746\) | −4.86253 | −0.178030 | ||||||||
\(747\) | 10.3132 | 0.377341 | ||||||||
\(748\) | 56.6988 | 2.07311 | ||||||||
\(749\) | −74.2344 | −2.71247 | ||||||||
\(750\) | 25.9507 | 0.947584 | ||||||||
\(751\) | 25.0729 | 0.914924 | 0.457462 | − | 0.889229i | \(-0.348759\pi\) | ||||
0.457462 | + | 0.889229i | \(0.348759\pi\) | |||||||
\(752\) | 37.2948 | 1.36000 | ||||||||
\(753\) | 30.2911 | 1.10387 | ||||||||
\(754\) | 162.902 | 5.93255 | ||||||||
\(755\) | 3.33172 | 0.121254 | ||||||||
\(756\) | 94.2782 | 3.42886 | ||||||||
\(757\) | 39.9659 | 1.45258 | 0.726292 | − | 0.687386i | \(-0.241242\pi\) | ||||
0.726292 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(758\) | 81.1527 | 2.94760 | ||||||||
\(759\) | −38.8525 | −1.41026 | ||||||||
\(760\) | 148.794 | 5.39732 | ||||||||
\(761\) | 12.4607 | 0.451699 | 0.225850 | − | 0.974162i | \(-0.427484\pi\) | ||||
0.225850 | + | 0.974162i | \(0.427484\pi\) | |||||||
\(762\) | −56.1395 | −2.03372 | ||||||||
\(763\) | 30.8385 | 1.11643 | ||||||||
\(764\) | 72.0585 | 2.60698 | ||||||||
\(765\) | −46.0883 | −1.66633 | ||||||||
\(766\) | −69.7112 | −2.51877 | ||||||||
\(767\) | −58.2720 | −2.10408 | ||||||||
\(768\) | 83.8882 | 3.02705 | ||||||||
\(769\) | 28.3942 | 1.02392 | 0.511960 | − | 0.859009i | \(-0.328920\pi\) | ||||
0.511960 | + | 0.859009i | \(0.328920\pi\) | |||||||
\(770\) | −159.455 | −5.74637 | ||||||||
\(771\) | 3.51678 | 0.126654 | ||||||||
\(772\) | −83.0292 | −2.98829 | ||||||||
\(773\) | 9.31668 | 0.335098 | 0.167549 | − | 0.985864i | \(-0.446415\pi\) | ||||
0.167549 | + | 0.985864i | \(0.446415\pi\) | |||||||
\(774\) | 64.5025 | 2.31850 | ||||||||
\(775\) | 53.5426 | 1.92331 | ||||||||
\(776\) | −74.7303 | −2.68266 | ||||||||
\(777\) | −7.32858 | −0.262911 | ||||||||
\(778\) | −82.3681 | −2.95304 | ||||||||
\(779\) | 39.0363 | 1.39862 | ||||||||
\(780\) | −275.123 | −9.85097 | ||||||||
\(781\) | 67.7832 | 2.42547 | ||||||||
\(782\) | −23.0934 | −0.825818 | ||||||||
\(783\) | 47.9456 | 1.71344 | ||||||||
\(784\) | 76.2316 | 2.72256 | ||||||||
\(785\) | 4.74335 | 0.169297 | ||||||||
\(786\) | −12.2471 | −0.436841 | ||||||||
\(787\) | 45.2900 | 1.61442 | 0.807208 | − | 0.590268i | \(-0.200978\pi\) | ||||
0.807208 | + | 0.590268i | \(0.200978\pi\) | |||||||
\(788\) | 33.2467 | 1.18436 | ||||||||
\(789\) | 27.1314 | 0.965904 | ||||||||
\(790\) | 6.31439 | 0.224656 | ||||||||
\(791\) | 69.5738 | 2.47376 | ||||||||
\(792\) | 130.753 | 4.64611 | ||||||||
\(793\) | −64.4830 | −2.28986 | ||||||||
\(794\) | −61.6920 | −2.18937 | ||||||||
\(795\) | 9.29627 | 0.329705 | ||||||||
\(796\) | 39.3759 | 1.39564 | ||||||||
\(797\) | −24.1518 | −0.855499 | −0.427749 | − | 0.903897i | \(-0.640693\pi\) | ||||
−0.427749 | + | 0.903897i | \(0.640693\pi\) | |||||||
\(798\) | 218.268 | 7.72661 | ||||||||
\(799\) | −15.8436 | −0.560507 | ||||||||
\(800\) | −29.9151 | −1.05766 | ||||||||
\(801\) | −58.9426 | −2.08264 | ||||||||
\(802\) | −45.0226 | −1.58980 | ||||||||
\(803\) | 11.8939 | 0.419727 | ||||||||
\(804\) | 62.1800 | 2.19292 | ||||||||
\(805\) | 44.7633 | 1.57770 | ||||||||
\(806\) | −148.557 | −5.23268 | ||||||||
\(807\) | 5.22135 | 0.183800 | ||||||||
\(808\) | −68.9604 | −2.42602 | ||||||||
\(809\) | −5.47453 | −0.192474 | −0.0962372 | − | 0.995358i | \(-0.530681\pi\) | ||||
−0.0962372 | + | 0.995358i | \(0.530681\pi\) | |||||||
\(810\) | 3.85673 | 0.135512 | ||||||||
\(811\) | −34.1169 | −1.19801 | −0.599004 | − | 0.800746i | \(-0.704436\pi\) | ||||
−0.599004 | + | 0.800746i | \(0.704436\pi\) | |||||||
\(812\) | 182.146 | 6.39208 | ||||||||
\(813\) | −2.53730 | −0.0889871 | ||||||||
\(814\) | −6.90569 | −0.242044 | ||||||||
\(815\) | 55.9676 | 1.96046 | ||||||||
\(816\) | 54.8840 | 1.92132 | ||||||||
\(817\) | 38.4007 | 1.34347 | ||||||||
\(818\) | 10.8934 | 0.380879 | ||||||||
\(819\) | −136.218 | −4.75986 | ||||||||
\(820\) | −79.8231 | −2.78754 | ||||||||
\(821\) | 1.64495 | 0.0574091 | 0.0287046 | − | 0.999588i | \(-0.490862\pi\) | ||||
0.0287046 | + | 0.999588i | \(0.490862\pi\) | |||||||
\(822\) | 11.0512 | 0.385455 | ||||||||
\(823\) | 6.81136 | 0.237429 | 0.118715 | − | 0.992928i | \(-0.462123\pi\) | ||||
0.118715 | + | 0.992928i | \(0.462123\pi\) | |||||||
\(824\) | −29.2816 | −1.02007 | ||||||||
\(825\) | 75.2652 | 2.62040 | ||||||||
\(826\) | −94.5332 | −3.28923 | ||||||||
\(827\) | −49.1504 | −1.70913 | −0.854563 | − | 0.519348i | \(-0.826175\pi\) | ||||
−0.854563 | + | 0.519348i | \(0.826175\pi\) | |||||||
\(828\) | −66.8447 | −2.32301 | ||||||||
\(829\) | −45.9876 | −1.59721 | −0.798607 | − | 0.601853i | \(-0.794429\pi\) | ||||
−0.798607 | + | 0.601853i | \(0.794429\pi\) | |||||||
\(830\) | −18.2158 | −0.632278 | ||||||||
\(831\) | 52.8149 | 1.83213 | ||||||||
\(832\) | −7.79756 | −0.270332 | ||||||||
\(833\) | −32.3848 | −1.12207 | ||||||||
\(834\) | −1.73628 | −0.0601226 | ||||||||
\(835\) | 6.97068 | 0.241230 | ||||||||
\(836\) | 141.758 | 4.90279 | ||||||||
\(837\) | −43.7233 | −1.51130 | ||||||||
\(838\) | 31.2667 | 1.08009 | ||||||||
\(839\) | −35.5172 | −1.22619 | −0.613095 | − | 0.790009i | \(-0.710076\pi\) | ||||
−0.613095 | + | 0.790009i | \(0.710076\pi\) | |||||||
\(840\) | −245.086 | −8.45626 | ||||||||
\(841\) | 63.6313 | 2.19418 | ||||||||
\(842\) | −59.8540 | −2.06270 | ||||||||
\(843\) | 70.1980 | 2.41775 | ||||||||
\(844\) | −45.8591 | −1.57853 | ||||||||
\(845\) | 104.996 | 3.61196 | ||||||||
\(846\) | −66.5373 | −2.28760 | ||||||||
\(847\) | −36.4881 | −1.25375 | ||||||||
\(848\) | −6.80456 | −0.233670 | ||||||||
\(849\) | −32.2223 | −1.10587 | ||||||||
\(850\) | 44.7365 | 1.53445 | ||||||||
\(851\) | 1.93861 | 0.0664546 | ||||||||
\(852\) | 189.729 | 6.50000 | ||||||||
\(853\) | 30.6390 | 1.04906 | 0.524529 | − | 0.851393i | \(-0.324241\pi\) | ||||
0.524529 | + | 0.851393i | \(0.324241\pi\) | |||||||
\(854\) | −104.609 | −3.57965 | ||||||||
\(855\) | −115.229 | −3.94076 | ||||||||
\(856\) | −107.516 | −3.67481 | ||||||||
\(857\) | 26.7959 | 0.915332 | 0.457666 | − | 0.889124i | \(-0.348686\pi\) | ||||
0.457666 | + | 0.889124i | \(0.348686\pi\) | |||||||
\(858\) | −208.827 | −7.12923 | ||||||||
\(859\) | 44.1114 | 1.50506 | 0.752531 | − | 0.658557i | \(-0.228833\pi\) | ||||
0.752531 | + | 0.658557i | \(0.228833\pi\) | |||||||
\(860\) | −78.5233 | −2.67762 | ||||||||
\(861\) | −64.2986 | −2.19129 | ||||||||
\(862\) | 20.7554 | 0.706932 | ||||||||
\(863\) | −21.1381 | −0.719548 | −0.359774 | − | 0.933040i | \(-0.617146\pi\) | ||||
−0.359774 | + | 0.933040i | \(0.617146\pi\) | |||||||
\(864\) | 24.4289 | 0.831087 | ||||||||
\(865\) | −28.1084 | −0.955713 | ||||||||
\(866\) | −30.1150 | −1.02335 | ||||||||
\(867\) | 24.1180 | 0.819092 | ||||||||
\(868\) | −166.106 | −5.63800 | ||||||||
\(869\) | 3.30339 | 0.112060 | ||||||||
\(870\) | −226.980 | −7.69535 | ||||||||
\(871\) | −33.5188 | −1.13574 | ||||||||
\(872\) | 44.6642 | 1.51252 | ||||||||
\(873\) | 57.8728 | 1.95870 | ||||||||
\(874\) | −57.7378 | −1.95301 | ||||||||
\(875\) | −15.6416 | −0.528781 | ||||||||
\(876\) | 33.2917 | 1.12482 | ||||||||
\(877\) | 13.3385 | 0.450409 | 0.225205 | − | 0.974311i | \(-0.427695\pi\) | ||||
0.225205 | + | 0.974311i | \(0.427695\pi\) | |||||||
\(878\) | −97.8372 | −3.30185 | ||||||||
\(879\) | −4.45757 | −0.150350 | ||||||||
\(880\) | −100.246 | −3.37929 | ||||||||
\(881\) | −25.9543 | −0.874421 | −0.437211 | − | 0.899359i | \(-0.644034\pi\) | ||||
−0.437211 | + | 0.899359i | \(0.644034\pi\) | |||||||
\(882\) | −136.004 | −4.57949 | ||||||||
\(883\) | 41.7160 | 1.40385 | 0.701927 | − | 0.712248i | \(-0.252323\pi\) | ||||
0.701927 | + | 0.712248i | \(0.252323\pi\) | |||||||
\(884\) | −85.5506 | −2.87738 | ||||||||
\(885\) | 81.1934 | 2.72929 | ||||||||
\(886\) | −6.08782 | −0.204524 | ||||||||
\(887\) | −5.28684 | −0.177515 | −0.0887573 | − | 0.996053i | \(-0.528290\pi\) | ||||
−0.0887573 | + | 0.996053i | \(0.528290\pi\) | |||||||
\(888\) | −10.6142 | −0.356188 | ||||||||
\(889\) | 33.8376 | 1.13488 | ||||||||
\(890\) | 104.108 | 3.48970 | ||||||||
\(891\) | 2.01766 | 0.0675941 | ||||||||
\(892\) | 35.4142 | 1.18576 | ||||||||
\(893\) | −39.6120 | −1.32557 | ||||||||
\(894\) | 105.758 | 3.53706 | ||||||||
\(895\) | −4.11619 | −0.137589 | ||||||||
\(896\) | −54.4940 | −1.82052 | ||||||||
\(897\) | 58.6231 | 1.95737 | ||||||||
\(898\) | 16.3173 | 0.544515 | ||||||||
\(899\) | −84.4738 | −2.81736 | ||||||||
\(900\) | 129.492 | 4.31639 | ||||||||
\(901\) | 2.89072 | 0.0963038 | ||||||||
\(902\) | −60.5883 | −2.01737 | ||||||||
\(903\) | −63.2516 | −2.10488 | ||||||||
\(904\) | 100.766 | 3.35141 | ||||||||
\(905\) | 38.4647 | 1.27861 | ||||||||
\(906\) | 7.07848 | 0.235167 | ||||||||
\(907\) | −7.12151 | −0.236466 | −0.118233 | − | 0.992986i | \(-0.537723\pi\) | ||||
−0.118233 | + | 0.992986i | \(0.537723\pi\) | |||||||
\(908\) | −58.1776 | −1.93069 | ||||||||
\(909\) | 53.4045 | 1.77132 | ||||||||
\(910\) | 240.596 | 7.97569 | ||||||||
\(911\) | −55.5357 | −1.83998 | −0.919990 | − | 0.391941i | \(-0.871804\pi\) | ||||
−0.919990 | + | 0.391941i | \(0.871804\pi\) | |||||||
\(912\) | 137.220 | 4.54382 | ||||||||
\(913\) | −9.52964 | −0.315385 | ||||||||
\(914\) | 34.0867 | 1.12749 | ||||||||
\(915\) | 89.8475 | 2.97027 | ||||||||
\(916\) | −67.8177 | −2.24076 | ||||||||
\(917\) | 7.38186 | 0.243771 | ||||||||
\(918\) | −36.5322 | −1.20574 | ||||||||
\(919\) | 21.9205 | 0.723090 | 0.361545 | − | 0.932355i | \(-0.382249\pi\) | ||||
0.361545 | + | 0.932355i | \(0.382249\pi\) | |||||||
\(920\) | 64.8318 | 2.13744 | ||||||||
\(921\) | −6.20889 | −0.204590 | ||||||||
\(922\) | 89.4868 | 2.94709 | ||||||||
\(923\) | −102.276 | −3.36644 | ||||||||
\(924\) | −233.496 | −7.68145 | ||||||||
\(925\) | −3.75547 | −0.123479 | ||||||||
\(926\) | −7.00307 | −0.230135 | ||||||||
\(927\) | 22.6763 | 0.744788 | ||||||||
\(928\) | 47.1968 | 1.54931 | ||||||||
\(929\) | 44.6819 | 1.46597 | 0.732983 | − | 0.680247i | \(-0.238128\pi\) | ||||
0.732983 | + | 0.680247i | \(0.238128\pi\) | |||||||
\(930\) | 206.991 | 6.78752 | ||||||||
\(931\) | −80.9681 | −2.65362 | ||||||||
\(932\) | −86.0089 | −2.81731 | ||||||||
\(933\) | 86.0625 | 2.81756 | ||||||||
\(934\) | 91.0005 | 2.97763 | ||||||||
\(935\) | 42.5866 | 1.39273 | ||||||||
\(936\) | −197.289 | −6.44858 | ||||||||
\(937\) | 16.1922 | 0.528975 | 0.264488 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264488 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(938\) | −54.3767 | −1.77546 | ||||||||
\(939\) | 72.5907 | 2.36891 | ||||||||
\(940\) | 81.0004 | 2.64194 | ||||||||
\(941\) | 17.6100 | 0.574069 | 0.287034 | − | 0.957920i | \(-0.407331\pi\) | ||||
0.287034 | + | 0.957920i | \(0.407331\pi\) | |||||||
\(942\) | 10.0776 | 0.328346 | ||||||||
\(943\) | 17.0087 | 0.553880 | ||||||||
\(944\) | −59.4309 | −1.93431 | ||||||||
\(945\) | 70.8125 | 2.30353 | ||||||||
\(946\) | −59.6017 | −1.93782 | ||||||||
\(947\) | −37.0787 | −1.20490 | −0.602448 | − | 0.798158i | \(-0.705808\pi\) | ||||
−0.602448 | + | 0.798158i | \(0.705808\pi\) | |||||||
\(948\) | 9.24638 | 0.300308 | ||||||||
\(949\) | −17.9463 | −0.582561 | ||||||||
\(950\) | 111.850 | 3.62889 | ||||||||
\(951\) | 38.0810 | 1.23486 | ||||||||
\(952\) | −76.2106 | −2.47000 | ||||||||
\(953\) | −14.9504 | −0.484290 | −0.242145 | − | 0.970240i | \(-0.577851\pi\) | ||||
−0.242145 | + | 0.970240i | \(0.577851\pi\) | |||||||
\(954\) | 12.1399 | 0.393045 | ||||||||
\(955\) | 54.1233 | 1.75139 | ||||||||
\(956\) | 14.0590 | 0.454700 | ||||||||
\(957\) | −118.745 | −3.83849 | ||||||||
\(958\) | 19.7804 | 0.639074 | ||||||||
\(959\) | −6.66103 | −0.215096 | ||||||||
\(960\) | 10.8647 | 0.350658 | ||||||||
\(961\) | 46.0347 | 1.48499 | ||||||||
\(962\) | 10.4197 | 0.335946 | ||||||||
\(963\) | 83.2626 | 2.68310 | ||||||||
\(964\) | −88.9084 | −2.86355 | ||||||||
\(965\) | −62.3634 | −2.00755 | ||||||||
\(966\) | 95.1028 | 3.05988 | ||||||||
\(967\) | −51.6886 | −1.66219 | −0.831097 | − | 0.556128i | \(-0.812286\pi\) | ||||
−0.831097 | + | 0.556128i | \(0.812286\pi\) | |||||||
\(968\) | −52.8467 | −1.69856 | ||||||||
\(969\) | −58.2940 | −1.87267 | ||||||||
\(970\) | −102.218 | −3.28203 | ||||||||
\(971\) | −10.3711 | −0.332824 | −0.166412 | − | 0.986056i | \(-0.553218\pi\) | ||||
−0.166412 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(972\) | 71.9395 | 2.30746 | ||||||||
\(973\) | 1.04653 | 0.0335502 | ||||||||
\(974\) | −56.6065 | −1.81379 | ||||||||
\(975\) | −113.565 | −3.63699 | ||||||||
\(976\) | −65.7654 | −2.10510 | ||||||||
\(977\) | 45.5204 | 1.45633 | 0.728163 | − | 0.685403i | \(-0.240374\pi\) | ||||
0.728163 | + | 0.685403i | \(0.240374\pi\) | |||||||
\(978\) | 118.907 | 3.80223 | ||||||||
\(979\) | 54.4643 | 1.74069 | ||||||||
\(980\) | 165.567 | 5.28884 | ||||||||
\(981\) | −34.5890 | −1.10434 | ||||||||
\(982\) | −1.93561 | −0.0617679 | ||||||||
\(983\) | 3.73183 | 0.119027 | 0.0595134 | − | 0.998228i | \(-0.481045\pi\) | ||||
0.0595134 | + | 0.998228i | \(0.481045\pi\) | |||||||
\(984\) | −93.1253 | −2.96873 | ||||||||
\(985\) | 24.9716 | 0.795663 | ||||||||
\(986\) | −70.5805 | −2.24774 | ||||||||
\(987\) | 65.2469 | 2.07683 | ||||||||
\(988\) | −213.893 | −6.80484 | ||||||||
\(989\) | 16.7318 | 0.532039 | ||||||||
\(990\) | 178.848 | 5.68416 | ||||||||
\(991\) | 21.8638 | 0.694527 | 0.347264 | − | 0.937768i | \(-0.387111\pi\) | ||||
0.347264 | + | 0.937768i | \(0.387111\pi\) | |||||||
\(992\) | −43.0405 | −1.36654 | ||||||||
\(993\) | −11.1703 | −0.354479 | ||||||||
\(994\) | −165.919 | −5.26263 | ||||||||
\(995\) | 29.5753 | 0.937602 | ||||||||
\(996\) | −26.6740 | −0.845197 | ||||||||
\(997\) | 31.1409 | 0.986242 | 0.493121 | − | 0.869961i | \(-0.335856\pi\) | ||||
0.493121 | + | 0.869961i | \(0.335856\pi\) | |||||||
\(998\) | 10.7863 | 0.341434 | ||||||||
\(999\) | 3.06675 | 0.0970276 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8003.2.a.c.1.12 | ✓ | 172 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.c.1.12 | ✓ | 172 | 1.1 | even | 1 | trivial |